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# Find General Solutions to a 2nd and 4th Order ODE

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A) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t)

b) y''+y=tcost

https://brainmass.com/math/trigonometry/general-solutions-order-ode-40462

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General solution to a 2nd + 4th order DE
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a) y'''' - 11y''' +45y"-81y'+54y = (t+1)e^(3t)
Solution. The characteristic equation is

Factoring it, we get

So, we get

So, the general solution to ODE: y'''' - 11y''' +45y"-81y'+54y =0 is

where a,b,c and d are constants.

Now in order to get the general solution to
y'''' - 11y''' +45y"-81y'+54y = ...

#### Solution Summary

General Solutions to a 2nd and 4th Order ODE are found. The solution is detailed and well presented.

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